摘要
A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function.In this paper, a conjecture on triangulation is confirmed. The relation between the piecewise linear algebraiccurve and four-color conjecture is also presented. By Morgan-Scott triangulation, we will show the instabilityof Bezout number of piecewise algebraic curves. By using the combinatorial optimization method, an upperbound of the Bezout number defined as the maximum finite number of intersection points of two piecewisealgebraic curves is presented.
A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function. In this paper, a conjecture on triangulation is confirmed. The relation between the piecewise linear algebraic curve and four-color conjecture is also presented. By Morgan-Scott triangulation, we will show the instability of Bezout number of piecewise algebraic curves. By using the combinatorial optimization method, an upper bound of the Bezout number defined as the maximum finite number of intersection points of two piecewise algebraic curves is presented.
基金
This work was supported by the National Natural Science Foundation of China(Grant Nos.19871010,69973010).
